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risk management financial

Questions and Answers of Risk Management Financial

7. What is the other solution mentioned in the text? What are the possible risks behind this solution?
6. What is a synthetic convertible?
5. How are the market professionals using reverse-convertibles? Why is there a “flood”?
4. What is a reverse-convertible bond? How would you decompose this instrument? How would a corporate treasurer use reverse-convertible bonds?
3. Give an example of a convertible bond issued, recently, in Europe. Discuss the main parameters. What is a conversion premium? What is the dilution effect?
2. What is a convertible bond? How would you decompose this instrument? How would a corporate treasurer use convertible bonds?
1. Let’s consider briefly some models of volatility. For example, what is the mean-reverting model for volatility? Are there any other models? Discuss briefly.
1. Read the article below carefully and answer the questions that follow.
4. Explain the purpose of the dislocation trades.
3. What are “balance-protected swaps”?
2. What does the reading mean by “dislocations”?
1. What is a corridor structure?
4. Explain carefully if this is true arbitrage. Are there any risks?
3. Show how you can do this using Bermudan options.
2. Show how you can hedge your Danish mortgage bond (DMB) positions in the swap and swaption markets and then earn a generous arbitrage. Why would this add liquidity to the Danish markets?
1. Define the following concepts: mortgage-backed security, prepayment risk, implicit option, and negative convexity.
1. The reading below deals with some typical swaption strategies and the factors that originate them. First, read it carefully.
10. Explain the following position using appropriate graphs. In particular, make sure that you define a barbell in credit sector. Finally, in what sense is this a convexity position? 1008 GMT [Dow
9. Consider the following news from Reuters: HVB Suggests Covered Bond Switches 0843 GMT [Dow Jones] LONDON—Sell DG Hyp 4.25% 2008s at 6.5 bp under swaps and buy Landesbank Baden-Wuerttemberg(LBBW)
8. We consider a reference portfolio of four investment grade names with the following one-year CDS rates: c(1) = 56 c(2) = 80 c(3) = 137 c(3) = 12 The recovery rate is the same for all names at R =
7. Consider the following news from Reuters: 1008 GMT [Dow Jones] LONDON—SG recommends selling 7-year 0–3% tranche protection versus buying 5-year and 10-year 0–3% protection. 7-year equity
6. We consider a reference portfolio of three investment grade names with the following one-year CDS rates: c(1) = 56 c(2) = 80 c(3) = 137 The recovery rate is the same for all names at R = 25. The
5. Consider the following quote: Until last year, this correlation pricing of single-tranche CDOs and first-todefault baskets was dependent on each bank or hedge fund’s assessment of correlation.
4. Consider the following news from Reuters: 1407GMT [Dow Jones] LONDON—According to a large investment bank investors can boost yields using the following strategies: (1) In the strategy, sell
3. We consider a reference portfolio of four investment grade names with the following one-year CDS rates: c(1) = 14 c(2) = 7 c(3) = 895 c(4) = 33 The recovery rate is the same for all names at R =
2. The iTraxx crossover index followed the path given below during three successive time periods: {330, 360, 320} Assume that there are 30 reference names in this portfolio. (a) You decide to select
1. We consider a reference portfolio of three investment grade names with the following one-year CDS rates: c(1) = 116 c(2) = 193 c(3) = 140 The recovery rate is the same for all names at R = 40. The
2. The iTraxx equity tranche spread followed the path given below during three successive time periods: {14, 15, 5, 16} Assume that there are 30 reference names in this portfolio. (a) You decide to
1. We consider a reference portfolio of three investment grade names with the following one-year CDS rates: c(1) = 15 c(2) = 11 c(3) = 330 The recovery rate is the same for all names at R = 40. The
3. Consider the following quote: Until last year, this correlation pricing of single-tranche CDOs and first-todefault baskets was dependent on each bank or hedge fund’s assessment of correlation.
2. Consider the following quote: It is only when portfolios are tranched that the relative value of default correlation becomes meaningful. So, for subordinate tranches, the risk and spreads
1. Consider the following news from Reuters: 1008 GMT [Dow Jones] LONDON—SG recommends selling 7-year 0–3% tranche protection versus buying 5-year and 10-year 0–3% protection. 7-year equity
4. Show how you would engineer the following CMS spread note. Issuer: ABC Notional: $10mio Tenor: 10 years Principal: Guaranteed at maturity Coupon: Yr 1: 11.50% Yr 2-10: 16 × (CMS30 − CMS10), max
3. Show how you would engineer the following Snowball Note. Issuer: ABC bank Notional: $10 mio Tenor: 10 years; Principal: Guaranteed at maturity Coupon: Yr 1; Q1: 9.00% Q2: Previous Coupon + CMS10
2. What follows is the description of a rather complex swap structured by a bank. The structure is sold for the purpose of liability management and involves an exotic option (digital cap) and a CMS
1. Consider the swap and Libor curves available in Reuters or Bloomberg. (a) Obtain the 3-month discount and forward curves (b) Obtain the 2-year forward curve (c) Find the components for the
2. Consider the following statement: One prop trader noted that cap/floor volatility should be slightly higher than swaptions. Corporates buy caps and investors sell swaptions through callable bonds,
1. Consider the following table displaying the bid-ask prices for all options on the OEX index passed on January 10, 2002, at 9:46. These options have February 22, 2002, expiry and at the time of
2. The following reading deals with another example of how spread positions on volatility can be taken. Yet, of interest here are further aspects of volatility positions. In fact, the episode is an
1. Read the quote carefully and describe how you would take this position using volatility swaps. Be precise about the parameters of these swaps. (a) How would you price this position? What does
3. Going back to the data given in Exercise 2, calculate the following: (a) The bid-ask on a forward swap that starts in two years with maturity in three years. The swap is against 12-month Libor.
2. You are given the following quotes for liquid swap rates. Assume that all time intervals are measured in years. Term Bid/Ask 2 6.2–6.5 3 6.4–6.7 4 7.0–7.3 5 7.5–7.8 6 8.1–8.4 You know
1. You are given the following quotes for liquid FRAs paid in arrears. Assume that all time intervals are measured in months of 30 days. Term Bid/Ask 3 × 6 4.5–4.6 6 × 9 4.7–4.8 9 × 12
4. Suppose you know that the current value of the peso-dollar exchange rate is 3.75 pesos per dollar. The yearly volatility of the Mexican peso is 20%. The Mexican interest rate is 8%, whereas the
3. Consider again the data given in the previous question. (a) Use Δ=1 year to discretize the system. (b) Generate five sets of standard normal random numbers with five random numbers in each set.
2. You know that the euro/dollar exchange rate et follows the real-world dynamics: det = μdt + .15etdWt (152) The current value of the exchange rate is eo = 1.1015. You also know that the price of a
1. You observe the following default-free discount bond prices B(t, Ti), where time is measured in years: B(0, 1) = 95, B(0, 2) = 93, B(0, 3) = 91, B(0, 4) = 89 (150) These prices are assumed to be
5. Barrier options belong to one of four main categories. They can be up-and-out, downand-out, up-and-in, or down-and-in. In each case, there is a specified “barrier,” and when the underlying
4. We use binomial trees to value American-style options on the British pound. Assume that the British pound is currently worth $1.40. Volatility is 20%. The current British risk-free rate is 6% and
3. Suppose the stock discussed in the previous exercise pays dividends. Assume all parameters are the same. Consider three forms of dividends paid by the firm: (a) The stock pays a continuous, known
2. Suppose you are given the following data. The risk-free interest rate is 4%. The stock price follows: dSt = μSt + σStdWt (124) The percentage annual volatility is 18% a year. The stock pays no
1. The current time is t = 1 and our framework is the Libor model. We consider a situation with four states of the world ωi at time t = 3. Suppose Li is the Libor process with a particular tenor and
5. The next question deals with a different type range option, called a range accrual option. Range accrual options can be used to take a view on volatility directly. When a trader is short
4. Double no-touch optionsis another name for range binaries. Read the following carefully, and then answer the questions at the end. Fluctuating U.S. dollar/yen volatility is prompting option
3. The following questions deal with range binaries. These are another example of exotic options. Read the following carefully and then answer the questions at the end. Investors are looking to
2. Consider this reading carefully and then answer the questions that follow. A bank suggested risk reversals to investors that want to hedge their Danish krone assets, before Denmark’s Sept. 28
1. Consider a bear spread. An investor takes a short position in a futures denoted by xt. But he or she thinks that xt will not fall below a level xmin. (a) How would you create a position that
11. Is this a true arbitrage? Are there any risks?
10. Do they have to hedge using caps only? Can floors do as well? Explain your answer graphically.
9. In particular, is this a position on the direction of rates or something else? In fact, can you explain why the professionals had to hedge their position using caps or floors?
8. Now the real issue. Explain the position taken by “knowledgeable” professionals.
7. What is a cap? What volatility do you buy or sell using caps?
6. What is the convexity adjustment for FRAs?
5. Describe the cash flows of FRAs. When are FRAs settled in the market?
2. What is meant by the convexity of long-dated interest rate swaps? 3. Explain the notion of convexity using a graph. 4. If bonds are convex, which fixed income instrument is not convex?
1. First the preliminaries. Explain what is meant by convexity of long-dated bonds.
5. Search the Internet for the following questions. (a) Which sensitivities do the Greeks, volga and Vanna represent? (b) Why are they relevant for vega hedging?
4. You are given the following table concerning the price of a put option satisfying all Black-Scholes assumptions. The strike is 20 and the volatility is 30%. The risk-free rate is 2.5%. Option
3. Consider the following episode: EUR/USD one-month implied volatility sank by 2.7% to 10% Wednesday as traders hedged this euro exposure against the greenback, as the euro plunged to historic lows
2. Consider the following quote: Implied U.S. dollar/New Zeland dollar volatility fell to 10.1%/11.1% on Tuesday. Traders bought at-the-money options at the beginning of the week, ahead of the
1. Consider the following comment dealing with options written on the euro-dollar exchange rate: Some traders, thinking that implied volatility was too high entered new trades. One example was to
3. Would there be ways DB can still take such a position? What are they?
2. Suppose these rules had been in effect during March, would they have prevented DB’s arbitrage position?
1. Eurex has made some changes in the Bund futures trading rules. What are these?
8. Explain how cheapest-to-deliver (CTD) bonds are determined. For needed information go to Web sites of futures exchanges.
7. Could taking a carefully chosen position in the relevant maturity FRA, offset the losses that shorts have suffered? Explain carefully.
6. Would an asset swap (e.g., swapping Libor against the relevant bond mentioned in the paper) have helped the shorts? Explain.
5. Why are penalties for failure to deliver relevant?
4. What is the importance of the size of ’05 Bund issue? How do traders “rustle up” such bonds to be delivered?
3. What is DB’s position aiming for?
2. Put this together with DB’s position in the repo market.
1. What is a calendar spread? Show DB’s position using cash flow diagrams.
3. A treasurer in Europe would like to borrow USD for 3 months. But instead of an outright loan, the treasurer decides to use the repo market. The company has holdings of Euro 40 million bonds. The
2. A dealer repos $10 million T-bills. The haircut is 5%. The parameters of the deal are as follows: • T-bill yield: 2% • Maturity of T-bills: 90 days • Repo rate: 2.5% term: 1 week (a) How
1. A dealer needs to borrow EUR 30 million. He uses a Bund as collateral. The Bund has the following characteristics: • Collateral 4.3% Bund, June 12, 2004 • Price: 100.50 • Start date:
7. Consider a 2-year currency swap between USD and EUR involving floating rates only. The EUR benchmark is selected as 6-month Euro Libor, the dollar benchmark is 6-month BBA Libor. You also have the
6. Foreigners buying Australian dollar instruments issued in Australia have to pay withholding taxes on interest earnings. This withholding tax can be exploited in tax-arbitrage portfolios using
5. Going back to Question 4, suppose you are given, in addition, data on FRAs both for USD and for EUR. Also suppose you are looking for arbitrage opportunities. Would these additional data be
4. Suppose at time t = 0, we are given prices for four zero-coupon bonds (B1, B2, B3, B4) that mature at times t = 1, 2, 3, and 4. This forms the term structure of interest rates. We also have the
3. You are a swap dealer and you have the following deals on your book: Long • 2-year receiver vanilla interest rate swap, at 6.75% p.a. 30/360. USD N = 50 million. • 3-year receiver vanilla
2. Read the following episode carefully. Italian Asset Swap Volumes Soar on Buyback Plans Volumes in the basis-swap spread market doubled last week as traders entered swaps in response to the Italian
1. You have a 4-year coupon bond that pays semiannual interest. The coupon rate is 8% and the par value is 100. (a) Can you construct a synthetic equivalent of this bond? Be explicit and show your
6. You are given the following information: 3-m Libor 3.2% 92 days 3 × 6 FRA 3.3%–3.4% 90 days 6 × 9 FRA 3.6%–3.7% 90 days 9 × 12 FRA 3.8%–3.9% 90 days (a) Show how to construct a synthetic
5. You are hired by a financial company in New Zealand and you have instant access to markets. You would like to lock in a 3-month borrowing cost in NZ$ for your client. You consider a NZ$ 1 × 4
4. Suppose practitioners learn that the British Banker’s Association (BBA) will change the panel of banks used to calculate the yen Libor. One or more of the “weaker” banks will be replaced by
3. A corporation will receive USD7 million in 3 months’ time for a period of 3 months. The current 3-month interest rate quotes are 5.67 to 5.61. The Eurodollar futures price is 94.90. Suppose in 3
2. The treasurer of a small bank has borrowed funds for 3 months at an interest rate of 6.73% and has lent funds for 6 months at 7.87%. The total amount is USD38 million. To cover his exposure
1. You have purchased 1 Eurodollar contract at a price of Q0 = 94.13, with an initial margin of 5%. You keep the contract for 5 days and then sell it by taking the opposite position. In the meantime,
6. Looking back, did Hong Kong drop the peg?
5. How do you plan to roll your position over?

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